Past Seminars: Spring 2016


  • February 9, 2016
    Zhong Wei Tang, Beijing Normal University
    Multiple solutions of Nonlinear Schrodinger equations involving critical exponent and potential wells
    In this talk, we will present some recent results about the existence and asymptotic behavior of the multiple solutions for the nonlinear Schrodinger equations such that the nonlinearity is critical growth and involving potential wells.

  • February 23, 2016
    Nathan Glatt-Holtz, Virginia Tech
    The Stochastic Boussinesq Equations and Applications in Turbulent Convection
    Buoyancy driven convection plays a ubiquitous role in physical applications: from cloud formation to large scale oceanic and atmospheric circulation pro- cesses to the internal dynamics of stars. Typically such fluid systems are driven by heat fluxes acting both through the boundaries (i.e. heating from below) and from the bulk (i.e. internal ’volumic’ heating) both of which can have an essentially stochastic nature in practice. In this talk we will review some recent results on invariant measures for the stochastic Boussinesq equations. These measures may be regarded as canonical objects containing important statistics associated with convection: mean heat transfer, small scale properties of the flow and pattern formation. We discuss ergodicity, uniqueness and singular parameter limits in this class of measures. Connections to the hypo-ellipticity theory of parabolic equations and to Wasser- stein metrics will be highlighted.

  • March 1, 2016
    Matias G. Delgadino, University of Maryland
    The Relationship Between the Obstacle Problem and Minimizers of the Interaction Energy
    The repulsion strength at the origin for repulsive/attractive potentials determines the minimal regularity of local minimizers of the interaction energy. If the repulsion is like Newtonian or more singular than Newtonian (but still locally integrable), then the local minimizers must be locally bounded densities (and even continuous for more singular than Newtonian repulsion). This can be achieved by first showing that the potential function associated to a local minimizer solves an obstacle problem and then by using classical regularity results for such problems.

  • March 8, 2016
    Michele Coti-Zelati, University of Maryland
    Enhanced dissipation and hypoellipticity in shear flows
    We analyze the decay and instant regularization properties of the evolution semigroups generated by two-dimensional drift-diffusion equations in which the scalar is advected by a shear flow and dissipated by full or partial diffusion. We consider both the case of space-periodic and the case of a bounded channel with no-flux boundary conditions. In the infinite Péclet number limit, our work quantifies the enhanced dissipation effect due to the shear. We also obtain hypoelliptic regularization, showing that solutions are instantly Gevrey regular even with only partial diffusion.

  • March 29, 2016
    Sagun Chanillo, Rutgers University
    The Fundamental Theorem of Calculus, Generalizations and Applications

  • April 12, 2016
    Dietmar Oelz, Courant Institute (NYU)
    TBA